The win snapped a two-game losing streak for the Eagles (7-4) heading into Wednesday's matchup with Massachusetts, which upset Memphis on Saturday.
Trapani and Raji both went 9-for-13 from the floor and Trapani had four of BC's 10 blocked shots.
Cecil Gresham led the Bulldogs (0-11), who entered the game as one of seven winless teams in the country, with 18 points. It was their 13th straight loss, dating to last season.
Bryant, in its second year in Division I, is coached by Tim O'Shea, who played at BC and worked under Eagles coach Al Skinner at both Rhode Island and BC.
The 46 points by Bryant, playing the first of six straight road games, matched the Bulldogs' season low.